// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include "solverbase.h"
#include <Eigen/QR>

template<typename MatrixType>
void
qr()
{
	STATIC_CHECK((internal::is_same<typename FullPivHouseholderQR<MatrixType>::StorageIndex, int>::value));

	static const int Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime;
	Index max_size = EIGEN_TEST_MAX_SIZE;
	Index min_size = numext::maxi(1, EIGEN_TEST_MAX_SIZE / 10);
	Index rows = Rows == Dynamic ? internal::random<Index>(min_size, max_size) : Rows,
		  cols = Cols == Dynamic ? internal::random<Index>(min_size, max_size) : Cols,
		  cols2 = Cols == Dynamic ? internal::random<Index>(min_size, max_size) : Cols,
		  rank = internal::random<Index>(1, (std::min)(rows, cols) - 1);

	typedef typename MatrixType::Scalar Scalar;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> MatrixQType;
	MatrixType m1;
	createRandomPIMatrixOfRank(rank, rows, cols, m1);
	FullPivHouseholderQR<MatrixType> qr(m1);
	VERIFY_IS_EQUAL(rank, qr.rank());
	VERIFY_IS_EQUAL(cols - qr.rank(), qr.dimensionOfKernel());
	VERIFY(!qr.isInjective());
	VERIFY(!qr.isInvertible());
	VERIFY(!qr.isSurjective());

	MatrixType r = qr.matrixQR();

	MatrixQType q = qr.matrixQ();
	VERIFY_IS_UNITARY(q);

	// FIXME need better way to construct trapezoid
	for (int i = 0; i < rows; i++)
		for (int j = 0; j < cols; j++)
			if (i > j)
				r(i, j) = Scalar(0);

	MatrixType c = qr.matrixQ() * r * qr.colsPermutation().inverse();

	VERIFY_IS_APPROX(m1, c);

	// stress the ReturnByValue mechanism
	MatrixType tmp;
	VERIFY_IS_APPROX(tmp.noalias() = qr.matrixQ() * r, (qr.matrixQ() * r).eval());

	check_solverbase<MatrixType, MatrixType>(m1, qr, rows, cols, cols2);

	{
		MatrixType m2, m3;
		Index size = rows;
		do {
			m1 = MatrixType::Random(size, size);
			qr.compute(m1);
		} while (!qr.isInvertible());
		MatrixType m1_inv = qr.inverse();
		m3 = m1 * MatrixType::Random(size, cols2);
		m2 = qr.solve(m3);
		VERIFY_IS_APPROX(m2, m1_inv * m3);
	}
}

template<typename MatrixType>
void
qr_invertible()
{
	using std::abs;
	using std::log;
	typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
	typedef typename MatrixType::Scalar Scalar;

	Index max_size = numext::mini(50, EIGEN_TEST_MAX_SIZE);
	Index min_size = numext::maxi(1, EIGEN_TEST_MAX_SIZE / 10);
	Index size = internal::random<Index>(min_size, max_size);

	MatrixType m1(size, size), m2(size, size), m3(size, size);
	m1 = MatrixType::Random(size, size);

	if (internal::is_same<RealScalar, float>::value) {
		// let's build a matrix more stable to inverse
		MatrixType a = MatrixType::Random(size, size * 2);
		m1 += a * a.adjoint();
	}

	FullPivHouseholderQR<MatrixType> qr(m1);
	VERIFY(qr.isInjective());
	VERIFY(qr.isInvertible());
	VERIFY(qr.isSurjective());

	check_solverbase<MatrixType, MatrixType>(m1, qr, size, size, size);

	// now construct a matrix with prescribed determinant
	m1.setZero();
	for (int i = 0; i < size; i++)
		m1(i, i) = internal::random<Scalar>();
	RealScalar absdet = abs(m1.diagonal().prod());
	m3 = qr.matrixQ(); // get a unitary
	m1 = m3 * m1 * m3;
	qr.compute(m1);
	VERIFY_IS_APPROX(absdet, qr.absDeterminant());
	VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}

template<typename MatrixType>
void
qr_verify_assert()
{
	MatrixType tmp;

	FullPivHouseholderQR<MatrixType> qr;
	VERIFY_RAISES_ASSERT(qr.matrixQR())
	VERIFY_RAISES_ASSERT(qr.solve(tmp))
	VERIFY_RAISES_ASSERT(qr.transpose().solve(tmp))
	VERIFY_RAISES_ASSERT(qr.adjoint().solve(tmp))
	VERIFY_RAISES_ASSERT(qr.matrixQ())
	VERIFY_RAISES_ASSERT(qr.dimensionOfKernel())
	VERIFY_RAISES_ASSERT(qr.isInjective())
	VERIFY_RAISES_ASSERT(qr.isSurjective())
	VERIFY_RAISES_ASSERT(qr.isInvertible())
	VERIFY_RAISES_ASSERT(qr.inverse())
	VERIFY_RAISES_ASSERT(qr.absDeterminant())
	VERIFY_RAISES_ASSERT(qr.logAbsDeterminant())
}

EIGEN_DECLARE_TEST(qr_fullpivoting)
{
	for (int i = 0; i < 1; i++) {
		CALL_SUBTEST_5(qr<Matrix3f>());
		CALL_SUBTEST_6(qr<Matrix3d>());
		CALL_SUBTEST_8(qr<Matrix2f>());
		CALL_SUBTEST_1(qr<MatrixXf>());
		CALL_SUBTEST_2(qr<MatrixXd>());
		CALL_SUBTEST_3(qr<MatrixXcd>());
	}

	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(qr_invertible<MatrixXf>());
		CALL_SUBTEST_2(qr_invertible<MatrixXd>());
		CALL_SUBTEST_4(qr_invertible<MatrixXcf>());
		CALL_SUBTEST_3(qr_invertible<MatrixXcd>());
	}

	CALL_SUBTEST_5(qr_verify_assert<Matrix3f>());
	CALL_SUBTEST_6(qr_verify_assert<Matrix3d>());
	CALL_SUBTEST_1(qr_verify_assert<MatrixXf>());
	CALL_SUBTEST_2(qr_verify_assert<MatrixXd>());
	CALL_SUBTEST_4(qr_verify_assert<MatrixXcf>());
	CALL_SUBTEST_3(qr_verify_assert<MatrixXcd>());

	// Test problem size constructors
	CALL_SUBTEST_7(FullPivHouseholderQR<MatrixXf>(10, 20));
	CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 10, 20>>(10, 20)));
	CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 10, 20>>(Matrix<float, 10, 20>::Random())));
	CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 20, 10>>(20, 10)));
	CALL_SUBTEST_7((FullPivHouseholderQR<Matrix<float, 20, 10>>(Matrix<float, 20, 10>::Random())));
}
